Analysis of Australian Electricity Loads Using Joint Bayesian Inference of D-Vines with Autoregressive Margins

Sklar's theorem allows the construction of models for dependent components using a multivariate copula together with marginal distributions. For estimation of the copula and marginal parameters, a two-step procedure is often used to avoid high-dimensional optimization. Here, marginal parameters are estimated first, then used to transform to uniform margins and in a second step, the copula parameters are estimated. This procedure is not efficient. Therefore, we follow a joint estimation approach in a Bayesian framework using Markov chain Monte Carlo (MCMC) methods. This allows also for the assessment of parameter uncertainty using credible intervals. D-vine copulae are utilized and as marginal models we allow for autoregressive models of first order. Finally, we apply these methods to Australian electricity loads, demonstrating the usefulness of this approach. Bayesian model selection is also discussed and applied using a method suggested by Congdon.